I was looking into what I could do for recourse if my landlord won't get the heat up to something reasonable, but when I looked further than just the tenants' handbook thing, it seems to me that I'm not covered at all. Can this be? If I live in a building older than 1952, does that mean I don't have any way to get the heat up? New York Multiple Residence Law article 3 doesn't mention anything about heat as far as I can see. I'm in Niagara Falls, and I can't find anything specific to the area either. I don't know what to do.

The Multiple Dwelling Law covers NYC. The Multiple Residence Law covers the rest of NYC. In addition, most of the large cities will have rules on minimum heat. Call your local city hall, or local council member who represents you and explain the situation. They should know specifics on local laws regarding heat.